CN116467556A - Harmonic impedance calculation method considering background harmonic voltage fluctuation and impedance variation - Google Patents
Harmonic impedance calculation method considering background harmonic voltage fluctuation and impedance variation Download PDFInfo
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Abstract
The invention discloses a harmonic impedance calculation method considering background harmonic voltage fluctuation and impedance change, which comprises the steps of firstly utilizing a cross correlation coefficient principle in time sequence clustering to enable harmonic voltage and harmonic current curves to be horizontally aligned, screening out data segments with smaller background harmonic fluctuation according to similarity, then utilizing a Pettitt method based on binary segmentation to detect a time point when harmonic impedance is suddenly changed for segmentation, and finally utilizing a regenerative weight least square method to calculate the harmonic impedance of segmented data. Simulation analysis proves that the method can well reduce adverse effects of background harmonic voltage fluctuation and impedance change on system harmonic impedance calculation, and has a wider application range.
Description
Technical Field
The invention relates to the technical field of electric power harmonic impedance calculation, in particular to a harmonic impedance calculation method considering background harmonic voltage fluctuation and impedance change.
Background
The construction of a novel power system taking new energy as a main body becomes a current research hot spot, and the novel power system causes the problems of increased harmonic content and increased frequency of the system due to the access of high-proportion new energy and high-proportion power electronic equipment, thereby causing the amplification of harmonic components and overrun of the harmonic components. Accurate system harmonic impedance calculation is a precondition for solving the harmonic problem. However, under the actual operation of the power system, the background harmonic voltage can fluctuate due to the fact that wind power generation is easily affected by wind speed, the photovoltaic power supply is easily affected by illumination intensity, power electronic devices are turned on and off, and the background harmonic voltage fluctuation can cause difficulty in accurate calculation of harmonic impedance. Moreover, the reasons such as the running mode of the power system is changed, the switching capacitor bank or the reactive compensation mode is changed, and the like can possibly cause the change of the harmonic impedance of the system, and the traditional calculation method has relatively less research on the change of the harmonic impedance of the system.
At present, the traditional harmonic impedance calculation method is mainly divided into two types of intervention type and non-intervention type. The intervention method utilizes the additional disturbance quantity artificially generated to be injected into the system or change the network topology structure of the system, and injects harmonic/inter-harmonic current, on-off branches or start-stop load into the system to estimate the harmonic impedance of the system. The main method for calculating the harmonic impedance of the current intervention system is as follows: a switched capacitor method, a thyristor branch switching method, a harmonic current source injection method, a switching element method, a user side parallel impedance method, an LCL resonance method and the like. The results obtained by the intervention method are accurate, but the disturbance injected by the injection method is possibly influenced by the system or adversely affects the operation of the system, and the cost of the intervention method is high, so the intervention method is not popularized and is widely used.
The non-intervention type harmonic impedance calculation method is widely adopted without influencing the normal operation of the system, and the harmonic impedance is calculated by utilizing the natural disturbance of the load or the system, the measurable parameters and the like. The existing method comprises the following steps: fluctuation amount method, linear regression method, independent component method, and covariance method. The fluctuation method is used for measuring the variation of the harmonic voltage and the harmonic current within a period of time, the ratio of the variation is used for approximately replacing the harmonic impedance, the method is simple to use, but the method is only suitable for occasions with relatively stable background harmonic waves and higher measuring precision of the harmonic voltage and the harmonic current; under the condition that the system background harmonic is basically stable, the regression method is based on the actual measured harmonic voltage and harmonic current data at the PCC, and a regression equation is constructed according to an equivalent circuit of the power system harmonic analysis, so that the system side harmonic impedance is calculated, but the method is difficult to maintain the robustness when the background harmonic fluctuation is large or the impact load is more; the independent component method utilizes the relation equation of the harmonic voltage and the harmonic current of the public coupling point and the harmonic currents of the system and the user side to calculate the harmonic impedance of the system, but the source signal needs to have non-Gaussian property; according to the characteristic that the harmonic current at the public connection point is weakly related to the system background harmonic, the covariance method uses the random vector covariance characteristic to counteract the background harmonic variation term in the deviation equation, so as to obtain the system side harmonic impedance, and the method is suitable for occasions in which the system side harmonic impedance is far smaller than the user side.
Since the linear regression method is widely used as it is also applicable to impedance calculation of a single harmonic source and a multi-harmonic source, data screening must be performed first when background harmonics fluctuate greatly. At present, it is generally considered that the harmonic impedance of a system is changed in a stepwise manner, namely, mutation occurs only at a certain time point and basically remains unchanged in a time period, and the current research mainly carries out sectional calculation by detecting the mutation point, but does not pay attention to the fact that the background harmonic wave greatly fluctuates to cause interference to detection, so that the detection result of the mutation point is affected.
In view of the above, the invention provides a non-intervention harmonic impedance calculation method considering background harmonic voltage fluctuation and impedance change, which utilizes a cross correlation coefficient in time sequence clustering and a Pettitt method based on binary segmentation to screen out a data segment with small background harmonic voltage fluctuation and relatively constant system harmonic impedance, and then adopts a regeneration weight least square method to perform stable regression, thereby reducing the influence of abnormal values on calculation results.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides the harmonic impedance calculation method considering the background harmonic voltage fluctuation and the impedance change, which can better reduce the adverse effect of the background harmonic voltage fluctuation and the impedance change on the calculation of the system harmonic impedance, can accurately calculate the system harmonic impedance under the condition of the background harmonic voltage fluctuation and the system impedance change, has wider application range and solves the problems in the background technology.
In order to achieve the above purpose, the present invention provides the following technical solutions: a harmonic impedance calculation method considering background harmonic voltage fluctuation and impedance variation comprises the following steps:
s1, screening out a period with smaller background harmonic voltage fluctuation based on a cross correlation coefficient in time sequence clustering;
s2, detecting and segmenting a time point when the harmonic impedance of the system is suddenly changed based on a binary segmentation Pettitt method;
s3, calculating the harmonic impedance of the system by adopting a regeneration weight least square method.
Preferably, in step S1, the screening the period with smaller background harmonic voltage fluctuation based on the cross correlation coefficient in the time sequence cluster is specifically: the harmonic voltage U and the harmonic current I are divided into n subsequences, cross correlation coefficients in a time sequence clustering K-Shape method are adopted for each subsequence to screen, and a distance measure SBD of the two subsequences is calculated to represent the similarity.
Preferably, the step S1 specifically includes:
according to the mutual correlation of the two sequences, the harmonic voltage curve of the public coupling point is fixedTime window, shift another harmonic current curve +.>Time window, curve for harmonic data->And->Performing globalAlignment:
wherein s is a harmonic current curveThe amount of translation of the time window; i.e m For harmonic current curve->Data point m above; m is harmonic current curve +.>Is a data length of (a) is a data length of (b).
According to harmonic current curveS.epsilon [ -m, m)]Obtaining harmonic current curve->And->Cross-correlation sequence:
wherein i is l Is a harmonic current curveData point i; u (u) l For harmonic voltage curve->Data point i; w is the current curve +.>W is sequentially increased from-m to m; k=w-m; k is E [ -m, m]。
When (when)When the maximum value is reached, the position of w is relative to +.>Is s' =w-m, the harmonic data curve +.>And->And carrying out per unit value processing after normalizing the cross-correlation sequence coefficients:
wherein, the liquid crystal display device comprises a liquid crystal display device,is->Is the maximum value of (2); />A harmonic current curve which is completely similar>Cross correlation values without relative displacement; />Is a completely similar harmonic voltage curve +.>Cross correlation values without relative displacement;the fluctuation range of (1) is [ -1,1]。
According toObtaining a calculation formula of the SBD distance:
wherein, the SBD value range is [0,2], and the smaller the SBD, the higher the similarity of the two curves, and the data period of the SBD approaching 0 is screened.
Preferably, the step S2 specifically includes:
s21, screening out a period with smaller background harmonic voltage fluctuation according to the step S1, and passing through a formula U pcc (n)＝Z s I pcc (n)+U s It is known that when the background harmonic voltage fluctuation is small, the system harmonic impedance is approximately estimated by equation (6):
wherein n is the sampling point sequence number; u (U) pcc (n) is the harmonic voltage at the PCC of the nth sample point; i pcc (n) harmonic current at PCC at the nth sampling point; z is Z s Is the system harmonic impedance; u (U) s Is the background harmonic voltage.
S22, in order to reduce the calculated amount, uniformly dividing the approximate estimated harmonic impedance value into n small segments, and performing mutation point inspection by using a Pettitt method based on binary segmentation;
s23, if no mutation point is detected or the detection significance probability p is more than 0.01, the system harmonic impedance is considered to be free from mutation in the time period;
s24, if the mutation point is detected or the detection significance probability p is smaller than 0.01, the system harmonic impedance is considered to be suddenly changed in the time period;
s25, judging whether one mutation point or a plurality of mutation points exist in the step S24, and segmenting the time sequence from the mutation points;
s26, carrying out Pettitt mutation test on the segmented data sequence, and if no mutation point is found, determining the mutation point detected in the step S24 as a true mutation point;
if a new mutation point is detected, a plurality of mutation points exist in the sequence in the step S24, and the detected mutation points deviate, the step S25 is returned to for circulation until all true mutation points are detected;
and S27, summarizing all detected true mutation points, and sequencing to obtain a detection final result.
Preferably, the Pettitt mutation test specifically includes: the sample data is divided into two subsequences at will, and the average value of the two subsequences is equal, namely, when the random variable sequence x is shown 1 ,x 2 ,…,x n Is arbitrarily divided into x 1 ,x 2 ,…,x m And x m+1 ,x m+2 ,…,x n After the two parts, if the distribution function F of the random variable in the two parts 1(x) ≠F 2(x) Mutations are considered to occur at m.
Preferably, the step S3 specifically includes: the calculation formula of the harmonic impedance of the system can be known by using a Norton circuit equivalent model:
U pcc (n)＝Z s I pcc (n)+U s (7)
data segment harmonic voltage U screened out by using cross correlation coefficient in time sequence clustering and Pettitt method based on binary segmentation pcc And I pcc Calculating coefficient Z by regeneration weight least square method s And U s 。
Preferably, the step of the regeneration right least square method includes the following steps:
1) Taking the harmonic current at the PCC as an independent variable, the harmonic voltage can be listed as a linear regression observation equation:
wherein, the liquid crystal display device comprises a liquid crystal display device,representing an observation matrix; beta is a coefficient matrix of the observation equation;/>is an unknown matrix; d is a constant term matrix of the observation equation; x is X 0 Is an approximation of the unknowns; />Is the value of the unknown; />
The error equation is:
wherein V represents the residual of the observed value Y; l is the error equation constant term; l= - (d+βx 0 -Y)。
2) The solution of the unknown number and the estimation value of the residual error and the unit weight variance of the observed value are obtained by the least square method:
V＝β(β T Pβ) -1 β T Pl-l (11)
wherein P represents the weight matrix of the observed value Y, and the main diagonal element is P j Initial value isLet n denote the number of observations, t denote the number of unknowns, r denote the number of redundant observations (degrees of freedom), i.e. r=n-t, r > 0.
3) Dividing formula (9) into two parts, wherein beta t For a full order matrix of t×t order, it is determined by linear transformation of the coefficient matrix β:
4) By deforming the formulae (13), (14):
V r ＝β rt V t -W rt (16)
in the method, in the process of the invention,
5) The absolute value of accidental error does not exceed a certain limit value, useTo limit the range of the unit weight true error, eta is called the threshold coefficient of the unit weight true error value range, and the estimated value V of the m (m- & gt infinity) group true error meeting the limiting condition (18) can be obtained by the formula (16) (1) ,V (2) ,…,V (m) The method comprises the following steps:
wherein, the liquid crystal display device comprises a liquid crystal display device,to->Is of initial value, & lt + & gt>Is the final value, ++>Take the value for step size, +.>Then it is determined by formula (16) that 2θ+1 is +.>In section->The number of the nodes of the middle value is +.>In the intervalOr->The number of the nodes of the middle value is half-cut number;
6) The reproduction variance is the variance calculated by using a plurality of estimated values of the true error of the same observed value, and the reproduction weight is the weight of the observed value calculated by using the reproduction variance of the observed value; the reproduction variance, the average value of the reproduction variance, and the reproduction right of the different observations are calculated according to the formulas (19), (20), and (21), respectively:
the beneficial effects of the invention are as follows: according to the method, firstly, harmonic voltage and harmonic current curves are horizontally aligned by utilizing a cross correlation coefficient principle in time sequence clustering, a data segment with smaller background harmonic fluctuation is screened out according to similarity, then, a time point at which harmonic impedance is suddenly changed is checked out by utilizing a Pettitt method based on binary segmentation for segmentation, and finally, harmonic impedance calculation is carried out on segmented data by utilizing a regenerative weight least square method. Adverse effects of background harmonic voltage fluctuation and impedance change on system harmonic impedance calculation can be well reduced, and the method has a wider application range.
Drawings
FIG. 1 is a sliding process diagram of a cross correlation coefficient method in time sequence clustering in the method of the invention;
FIG. 2 is a diagram of a Norton equivalent circuit in the method of the present invention;
FIG. 3 is a schematic diagram of the system harmonic impedance variation in the method of the present invention;
FIG. 4 is a schematic representation of the shift in the Pettitt test mutation points in the method of the invention;
FIG. 5 is a schematic diagram of a true mutation point detected by a Pettitt method based on binary segmentation in the method of the invention;
FIG. 6 is a flow chart of a method for calculating harmonic impedance taking background harmonic voltage fluctuation and impedance variation into consideration;
FIG. 7 is a graph of the magnitude of the 5 th harmonic voltage and current at the PCC, with FIG. 7 (a) being the magnitude of the harmonic voltage and FIG. 7 (b) being the magnitude of the harmonic current, in an embodiment of the present invention;
FIG. 8 is a diagram of the result of the Pettitt method test based on binary segmentation in the embodiment of the present invention, wherein FIG. 8 (a) shows that the mutation point is at 4 seconds, FIG. 8 (b) shows that the mutation point is at 8 seconds, and FIG. 8 (c) shows that the mutation point is at 12 seconds;
FIG. 9 is a graph comparing the calculation results of the method according to the embodiment of the present invention with those of other methods.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Example 1
According to the harmonic impedance calculation method considering background harmonic voltage fluctuation and impedance change, firstly, the mutual correlation coefficient in time sequence clustering is utilized to conduct translation alignment on harmonic voltage and harmonic current curves at public connection points (Point of Common Connection and PCC) and check similarity, a period of time with relatively stable background harmonic voltage is screened out, then harmonic impedance mutation check is conducted on screened data through a Pettitt method based on binary segmentation, segmentation is conducted according to the detected true mutation points, and finally, the system harmonic impedance of each segment is calculated through a regeneration right least square method.
The harmonic impedance calculation method taking the background harmonic voltage fluctuation and the impedance change into consideration, as shown in fig. 6, comprises the following steps:
step1, screening out a period with smaller background harmonic voltage fluctuation based on the cross correlation coefficient;
step2 detects and segments a time point when the harmonic impedance of the system is suddenly changed based on a binary segmentation Pettitt method;
step3, calculating the system harmonic impedance by adopting a regeneration weight least square method.
By the harmonic impedance calculation method considering the background harmonic voltage fluctuation and the impedance change, the system harmonic impedance can be calculated more accurately under the condition of the background harmonic voltage fluctuation and the impedance change.
Further, step1 includes: the harmonic voltage U and the harmonic current I are divided into n subsequences, cross correlation coefficients in a time sequence clustering (K-Shape) method are adopted for each subsequence to screen, and distance measures (Shape Based Distance, SBD) of the two subsequences are calculated to represent the similarity.
In a specific embodiment, in the harmonic impedance calculation method Step1 taking the background harmonic voltage fluctuation and the impedance change into consideration, the screening of the data segment with smaller background harmonic voltage fluctuation by using the cross correlation coefficient in the time sequence cluster includes:
the general electric power system is complex, and the system side and the user side can be equivalent toThe analysis is performed by a norton circuit as shown in fig. 2. In FIG. 2, U PCC And I PCC Respectively representing the harmonic voltage and the harmonic current at PCC, I s And I c Equivalent harmonic current sources respectively representing the system side and the user side, Z s And Z c Representing the system-side and user-side equivalent harmonic impedances, respectively.
From the following relation, it can be seen that
U PCC ＝Z s I PCC +U s (22)
When the system side harmonic source fluctuation is small, the harmonic current I at the PCC PCC Mostly by user side I c Is provided at this time U PCC And I PCC Exhibits strong positive correlation due to I s And I c Independent of each other for a period of time, the inverse of the above conclusion is still true, i.e. if U PCC And I PCC The method has strong positive correlation and relatively stable background harmonic, so that the method can be used for screening out the data segments meeting the conditions for calculation.
Due to the harmonic voltage U at PCC PCC And harmonic current I PCC The phase drift exists, and the correlation between the two is directly calculated with larger error, so that the correlation strength of the two is accurately represented by selecting the cross correlation coefficient in the time sequence cluster to carry out curve similarity test.
According to the mutual correlation of the two sequences, the harmonic voltage curve of the public coupling point is fixedTime window, shift another harmonic current curve +.>Time window, as shown in FIG. 1, for harmonic data curve +.>And->Global alignment is performed:
wherein i is l Is a harmonic current curveData point i; u (u) l For harmonic voltage curve->Data point i; w is the current curve +.>W is sequentially increased from-m to m; k=w-m; k is E [ -m, m]。
According to harmonic current curveS.epsilon [ -m, m)]Obtaining harmonic current curve->And->Cross-correlation sequence:
wherein i is l Is a harmonic current curveData point i; u (u) l For harmonic voltage curve->Data point i; k is E [ -m, m]The method comprises the steps of carrying out a first treatment on the surface of the w is sequentially increased from-m to m.
When (when)When the maximum value is reached, the position of w is relative to +.>Is s' =w-m, the harmonic data curve +.>And->And carrying out per unit value processing after normalizing the cross-correlation sequence coefficients:
wherein, the liquid crystal display device comprises a liquid crystal display device,is->Is the maximum value of (2); />A harmonic current curve which is completely similar>Cross correlation values without relative displacement; />Is a completely similar harmonic voltage curve +.>Cross correlation values without relative displacement;the fluctuation range of (1) is [ -1,1]。
According toObtaining a calculation formula of the SBD distance:
the SBD value range is [0,2], the smaller the SBD, the higher the similarity of the two curves, and the data segment of which the SBD is close to 0 is screened out, so that the influence of background harmonic voltage fluctuation can be reduced, and the system harmonic impedance value can be accurately calculated.
In a specific embodiment, in the harmonic impedance calculation method Step2 of the present invention, which considers background harmonic voltage fluctuation and impedance variation, the use of the Pettitt method based on binary segmentation to verify harmonic impedance mutation points includes:
in fact, the system harmonic impedance may be changed due to the change of the operation mode of the power system, the change of the switching capacitor bank or the reactive compensation mode, etc., so it is currently generally considered that the system harmonic impedance is changed in stages, that is, only a sudden change occurs at a certain time point and remains unchanged basically in a time period, as shown in fig. 3, that is, only the time point at which the sudden change occurs needs to be checked and the system harmonic impedance value needs to be calculated in segments.
The Pettitt mutation test method is a non-parameter statistical test method based on rank, is simple and convenient to calculate, can determine mutation time points, and can better identify mutation points of sequences. The basic principle of the Pettitt mutation test method is that the sample data is arbitrarily divided into two subsequences, and the average value of the two subsequences is equal, namely, when the random variable sequence x is shown 1 ,x 2 ,…,x n Is arbitrarily divided into x 1 ,x 2 ,…,x m And x m+1 ,x m+2 ,…,x n After the two parts, if the distribution function F of the random variable in the two parts 1(x) ≠F 2(x) Mutations are considered to occur at m, which is defined as follows:
wherein:
statistics U t,N Ji Suanle the number of times the first sample sequence is greater than the second sample sequence corresponds to |U at the most significant mutation point t t,n Maximum of I, here K n The representation is:
K n ＝Max 1≤t≤n |U t,n | (25)
the corresponding saliency probability can be calculated approximately by the following formula:
since the Pettitt mutation test method can only identify one mutation point in a long sequence, a plurality of mutation points may exist in a harmonic impedance sequence, and if the harmonic impedance sequence is large, the calculation amount of the method is large. The invention improves the Pettitt mutation test method based on the binary segmentation method, so that all mutation points can be identified, and the calculated amount is reduced. The binary segmentation method (Binary Segmentation, BS), which is commonly used in the fields of data segmentation and image segmentation, is a processing method for iterative detection.
Further, the specific steps of mutation detection based on the binary segmentation Pettitt method comprise:
(1) Because the Step1 process has screened out the period of small background harmonic voltage fluctuation, the method is carried out according to the formula U pcc (n)＝Z s I pcc (n)+U s It is known that when the background harmonic voltage is small, the system harmonic impedance can be approximated by:
(2) In order to reduce the calculated amount, the approximate estimated harmonic impedance value is uniformly divided into n small segments, and the mutation point inspection is performed by using a Pettitt method based on binary segmentation.
(3) If no abrupt point is detected or the probability of detection significance p > 0.01, then it is assumed that no abrupt change in system harmonic impedance occurs during this time period.
(4) If the mutation point is detected or the detection significance probability p is less than 0.01, the system harmonic impedance is considered to be suddenly changed in the time period.
(5) In the step (4), whether there is a mutation point or a plurality of mutation points needs to be judged again, and the time sequence is segmented from the mutation points.
(6) And (3) carrying out Pettitt mutation detection on the segmented data sequence, if no mutation point is found, the mutation point detected in the step (4) is a true mutation point, if a new mutation point is detected, a plurality of mutation points exist in the sequence in the step (4), the detected mutation points are shifted, as shown by the m point in fig. 4, and the step (5) is returned to carry out circulation until all the true mutation points are detected, as shown by the i and j points in fig. 5.
(7) All detected true mutation points are summarized and sequenced as the final detection result.
In one specific embodiment, in the harmonic impedance calculation method Step3 of the present invention, which considers background harmonic voltage fluctuation and impedance variation, the calculation of the harmonic impedance of the system by using the regenerative weight least square method includes:
the regeneration weight least square method (self-born weighted least squares method, SBWLS) is a new robust regression estimation method, which constructs the weight of the observed value by using effective information provided by a residual error condition equation of the observed value, rather than constructing the weight of the observed value by using the residual error of the observed value obtained by a least square method like a general traditional method, and when a plurality of abnormal values exist, the regeneration weight least square method can more effectively eliminate or weaken the influence of the abnormal values on parameter estimation compared with the general robust regression method.
Taking the harmonic current at the PCC as an independent variable, the harmonic voltage can be listed as a linear regression observation equation:
wherein, the liquid crystal display device comprises a liquid crystal display device,representing an observation matrix; beta is a coefficient matrix of the observation equation; />Is an unknown matrix; d is a constant term matrix of the observation equation; x is X 0 Is an approximation of the unknowns; />Is the value of the unknown; />
The error equation is:
wherein V represents the residual of the observed value Y; l is the error equation constant term; l= - (d+βx 0 -Y)。
The solution of the unknown number and the estimation of the residual error and unit weight variance of the observed value can be obtained by the least square method:
V＝β(β T Pβ) -1 β T Pl-l (11)
wherein P represents the weight matrix of the observed value Y, and the main diagonal element is P j Initial value is Let n denote the number of observations, t denote the number of unknowns, r denote the number of redundant observations (degree of freedom), i.e. r=n-t, r > 0
Dividing formula (9) into two parts, wherein beta t The full order matrix of t×t order can be determined by linearly transforming the coefficient matrix β.
Deforming the formula (13) to obtain
Substitution of formula (15) into formula (14)
V r ＝β rt V t -W rt (16)
In the method, in the process of the invention,
since the absolute value of the accidental error does not exceed a certain limit valueThe range of the unit weight true error is limited, and eta is called a threshold coefficient of the unit weight true error value range. From equation (16), an estimate V of the true error of the m (m→infinity) group satisfying the constraint (18) can be obtained (1) ,V (2) ,…,V (m) The method comprises the following steps:
in the actual calculation of the number of the points,to->Is of initial value, & lt + & gt>Is the final value, ++>Take the value for step size, +.>Then it is determined by equation (16). 2 theta +1 is->In section->The number of the nodes of the middle value is +.>In section->Or->The number of nodes of the intermediate value is called half-cut number.
The regenerated variance is the variance calculated from multiple (m) estimates of true errors of the same observed value. The reproduction right is a right of the observed value calculated from the reproduction variance of the observed value.
The reproduction variance, the average value of the reproduction variance, and the reproduction weight of the different observations are calculated according to equations (19), (20), and (21), respectively.
Equation (16) is referred to as a regeneration weight function equation, and equation (18) is referred to as a regeneration weight function constraint. Different parameter estimation problems have different regeneration weight functions and the same regeneration weight function constraints. The threshold coefficient eta and the half node number theta of the two basic parameter values are determined by a simulation experiment method. M will not be infinite due to the constraint of the half-node number θ. Beta t And beta r There is non-uniqueness but no significant impact on the parameter estimation results.
From the linear relation of system harmonic impedance
Wherein, the liquid crystal display device comprises a liquid crystal display device,an estimated value of the ith harmonic voltage; i.e i Is the i-th harmonic current observation; u (u) s The background harmonic voltage is to be solved; z s Is the system harmonic impedance to be solved.
From the following componentsIs available in the form of
u i +v i ＝1·u s +i i ·z s (28)
Wherein u is i Is the true value of the ith harmonic voltage; v i Is the ith harmonic voltage residual.
Matrixing the above
In this linear regression model, n is the number of observations, where the number of weights to be found t=2. The unitary linear regression model error equation is as follows:
and (3) performing linear transformation on the coefficient matrix beta in the error equation (9) to determine t=2 error equations forming the maximum linear independent group. The 2 error equations that make up the maximum linear independent set are not unique, and any one set is sufficient.
The blocking matrix of the model error equation is as follows
The regeneration weight function from equation (30) is:
V r ＝A t V t -W (32)
wherein V is r ＝[v u3 … v un ] T ＝[v 3 … v n ] T ,W＝-(A t l t -l r )，V t ＝[v u1 v u2 ] T ＝[v 1 v 2 ] T 。
Using the regeneration weight of the observed value obtained in the formula (32) as the weight of the observed value of the next iteration, performing iterative calculation by using a least square method, and if the iteration termination condition is that the residual error of the observed value of two adjacent times is smaller than 0.1, obtaining a background harmonic voltage u according to the formula (10) s And system harmonic impedance z s Approximating a true value.
Example 2
The technical effects of the present invention will be described below by way of a specific example. An equivalent circuit model shown in fig. 2 is built on a MATLAB software platform, five-order harmonic is taken as an example, harmonic source and harmonic impedance parameters in the simulation model are set as follows, and first harmonic voltage and harmonic current are measured every 0.02s, and 16s are simulated.
A harmonic source:is 120A, ">Is 12A>Is-30 DEG,/v>Is 70 deg.. Administering +.>Adding a random disturbance of + -10% relative to its magnitude; its phase angle plus a random perturbation of + -10% relative to the phase angle size. Give->Amplitude plus + 5% random disturbance; give->Phase angle plus + 5% random perturbation.
Harmonic impedance: in order to simulate abrupt change of harmonic impedance, the harmonic impedance value is greatly changed every 4s, and the system side harmonic impedance Z is 0-4 s s Set as (15+j20) omega, 4-8 s system side harmonic impedance Z s Set as (30+j40) Ω, 8-12 s system side harmonic impedance Z s Set as (45+j60) omega, 12-16 s system side harmonic impedance Z s Set to (15+10) Ω.
Measuring harmonic voltage and current values at PCC, dividing amplitude curves into n subsequences as shown in FIG. 7 (a) and FIG. 7 (b), calculating SBD values of each subsequence by using cross correlation coefficients of time sequence clustering, screening out data segments with SBD less than 0.2, using harmonic voltage to harmonic current to approximately replace harmonic impedance values, and using a Pettitt method based on binary segmentation to test mutation points.
The test results are shown in fig. 8 (a), 8 (b) and 8 (c). It can be clearly seen from the graph that harmonic impedance mutation points occur at 4s, 8s and 12s and are consistent with the impedance mutation points set above, so that the method can effectively identify the time point when the harmonic impedance is suddenly changed, then segments the time point according to the mutation points, calculates the harmonic impedance value of each segment by using a regeneration weight least square method and robust regression, and calculates the calculation result and the error percentage as shown in table 1, and can calculate the harmonic impedance value of the system more accurately as shown in table 1.
TABLE 1
When a plurality of abnormal values exist in the data, the regenerative weight least square method adopted by the invention has robustness compared with other methods, and the data segments with more than 3 abnormal values are selected to be used for carrying out 50 repeated experiments by utilizing a fluctuation amount method (method 1), a robust regression method (method 2), an independent component method (method 3) and a covariance method (method 4) in comparison with a harmonic impedance calculation method (method 5) which considers background harmonic voltage fluctuation and impedance change and is proposed by the invention, wherein the calculation result is shown in the following figure 9.
As can be seen from fig. 9, the method of calculating the harmonic impedance of the system by using the data filtered by the time-series clustering cross correlation coefficient and then using the regenerative weight least square method is superior to other four methods, and has more robustness to the existence of a plurality of abnormal values.
The invention provides a harmonic impedance calculation method considering background harmonic voltage fluctuation and impedance change, which is suitable for impedance calculation of a single harmonic source and a plurality of harmonic sources. According to simulation results, when the background harmonic voltage fluctuates, the cross correlation coefficient of the proposed time sequence cluster can align the harmonic voltage and the current in a translation way and screen out the data segment meeting the conditions, and compared with the traditional pearson correlation coefficient method, the error can be reduced better. When the system impedance changes, the proposed Pettitt method based on binary segmentation can effectively screen out the time point when the harmonic impedance changes suddenly, and the effect is better than that of a general inspection method. When there are multiple outliers, the regenerative weight least squares method is more robust than other methods. Therefore, the method provided by the invention can reduce adverse effects on impedance calculation caused by background harmonic voltage fluctuation and system harmonic impedance change, and has a wider application range.
Although the present invention has been described with reference to the foregoing embodiments, it will be apparent to those skilled in the art that modifications may be made to the embodiments described, or equivalents may be substituted for elements thereof, and any modifications, equivalents, improvements and changes may be made without departing from the spirit and principles of the present invention.
Claims (7)
1. A harmonic impedance calculation method taking background harmonic voltage fluctuation and impedance change into consideration is characterized by comprising the following steps:
s1, screening out a period with smaller background harmonic voltage fluctuation based on a cross correlation coefficient in time sequence clustering;
s2, detecting and segmenting a time point when the harmonic impedance of the system is suddenly changed based on a binary segmentation Pettitt method;
s3, calculating the harmonic impedance of the system by adopting a regeneration weight least square method.
2. The harmonic impedance calculation method considering background harmonic voltage fluctuation and impedance variation according to claim 1, wherein: in step S1, the screening the period with smaller background harmonic voltage fluctuation based on the cross correlation coefficient in the time sequence cluster specifically includes: the harmonic voltage U and the harmonic current I are divided into n subsequences, cross correlation coefficients in a time sequence clustering K-Shape method are adopted for each subsequence to screen, and a distance measure SBD of the two subsequences is calculated to represent the similarity.
3. The harmonic impedance calculation method considering background harmonic voltage fluctuation and impedance variation according to claim 1, wherein: the step S1 specifically includes:
according to the mutual correlation of the two sequences, the harmonic voltage curve of the public coupling point is fixedTime window, shift another harmonic current curve +.>Time window, curve for harmonic data->And->Global alignment is performed:
wherein s is a harmonic current curveThe amount of translation of the time window; i.e m For harmonic current curve->Data point m above; m is harmonic current curve +.>Is a data length of (a);
according to harmonic current curveS.epsilon [ -m, m)]Obtaining harmonic current curve->And->Cross-correlation sequence:
wherein i is l Is a harmonic current curveData point i; u (u) l For harmonic voltage curve->Data point i; w is the current curve +.>W is sequentially increased from-m to m; k=w-m; k is E [ -m, m]；
When (when)When the maximum value is reached, the position of w is relative to +.>Is s' =w-m, the harmonic data curve +.>And->Cross-correlationAnd (3) carrying out per unit value processing after normalizing the sequence coefficients:
wherein, the liquid crystal display device comprises a liquid crystal display device,is->Is the maximum value of (2); />A harmonic current curve which is completely similar>Cross correlation values without relative displacement; />Is a completely similar harmonic voltage curve +.>Cross correlation values without relative displacement;the fluctuation range of (1) is [ -1,1]；
According toObtaining a calculation formula of the SBD distance:
wherein, the SBD value range is [0,2], and the smaller the SBD, the higher the similarity of the two curves, and the data period of the SBD approaching 0 is screened.
4. The harmonic impedance calculation method considering background harmonic voltage fluctuation and impedance variation according to claim 1, wherein: the step S2 specifically includes:
s21, screening out a period with smaller background harmonic voltage fluctuation according to the step S1, and passing through a formula U pcc (n)＝Z s I pcc (n)+U s It is known that when the background harmonic voltage is small, the system harmonic impedance is approximately estimated by equation (6);
wherein n is the sampling point sequence number; u (U) pcc (n) is the harmonic voltage at the PCC of the nth sample point; i pcc (n) harmonic current at PCC at the nth sampling point; z is Z s Is the system harmonic impedance; u (U) s Is background harmonic voltage;
s22, in order to reduce the calculated amount, uniformly dividing the approximate estimated harmonic impedance value into n small segments, and performing mutation point inspection by using a Pettitt method based on binary segmentation;
s23, if no mutation point is detected or the detection significance probability p is more than 0.01, the system harmonic impedance is considered to be free from mutation in the time period;
s24, if the mutation point is detected or the detection significance probability p is smaller than 0.01, the system harmonic impedance is considered to be suddenly changed in the time period;
s25, judging whether one mutation point or a plurality of mutation points exist in the step S24, and segmenting the time sequence from the mutation points;
s26, carrying out Pettitt mutation test on the segmented data sequence, and if no mutation point is found, determining the mutation point detected in the step S24 as a true mutation point;
if a new mutation point is detected, a plurality of mutation points exist in the sequence in the step S24, and the detected mutation points deviate, the step S25 is returned to for circulation until all true mutation points are detected;
and S27, summarizing all detected true mutation points, and sequencing to obtain a detection final result.
5. The method for calculating harmonic impedance taking into account background harmonic voltage fluctuations and impedance variations according to claim 4, wherein: the Pettitt mutation test specifically comprises the following steps: the sample data is divided into two subsequences at will, and the average value of the two subsequences is equal, namely, when the random variable sequence x is shown 1 ,x 2 ,…,x n Is arbitrarily divided into x 1 ,x 2 ,…,x m And x m+1 ,x m+2 ,…,x n After the two parts, if the distribution function F of the random variable in the two parts 1(x) ≠F 2(x) Mutations are considered to occur at m.
6. The harmonic impedance calculation method considering background harmonic voltage fluctuation and impedance variation according to claim 1, wherein: the step S3 specifically includes: the calculation formula of the harmonic impedance of the system can be known by using a Norton circuit equivalent model:
U pcc (n)＝Z s I pcc (n)+U s (7)
data segment harmonic voltage U screened out by using cross correlation coefficient in time sequence clustering and Pettitt method based on binary segmentation pcc And I pcc Calculating coefficient Z by regeneration weight least square method s And U s 。
7. The harmonic impedance calculation method considering background harmonic voltage fluctuation and impedance variation according to claim 6, wherein: the step of the regeneration weight least square method comprises the following steps:
1) Taking the harmonic current at the PCC as an independent variable, and listing a linear regression observation equation by taking the harmonic voltage as the independent variable as follows:
wherein, the liquid crystal display device comprises a liquid crystal display device,representing an observation matrix; beta is a coefficient matrix of the observation equation; />Is an unknown matrix; d is a constant term matrix of the observation equation; x is X 0 Is an approximation of the unknowns; />Is the value of the unknown; />
The error equation is:
wherein V represents the residual of the observed value Y; l is the error equation constant term; l= - (d+βx 0 -Y)；
2) The solution of the unknown number and the estimation value of the residual error and the unit weight variance of the observed value are obtained by the least square method:
V＝β(β T Pβ) -1 β T Pl-l (11)
wherein P represents the weight matrix of the observed value Y, and the main diagonal element is P j Initial value isLet n denote the number of observations, t denote the number of unknowns, r denote the number of redundant observations, i.e. r=n-t, r > 0;
3) Dividing formula (9) into two parts, wherein beta t For a full order matrix of t×t order, it is determined by linear transformation of the coefficient matrix β:
4) By deforming the formulae (13), (14):
V r ＝β rt V t -W rt (16)
in the method, in the process of the invention,
5) The absolute value of accidental error does not exceed a certain limit value, useTo limit the range of the unit weight true error, eta is called the threshold coefficient of the unit weight true error value range, and the estimated value V of the m (m- & gt infinity) group true error meeting the limiting condition (18) can be obtained by the formula (16) (1) ,V (2) ,…,V (m) The method comprises the following steps:
wherein, the liquid crystal display device comprises a liquid crystal display device,to->Is of initial value, & lt + & gt>Is the final value, ++>Take the value for step size, +.>Then it is determined by formula (16) that 2θ+1 is +.>In section->The number of the nodes of the middle value is +.>In section->Or (b)The number of the nodes of the middle value is half-cut number;
6) The reproduction variance is the variance calculated by using a plurality of estimated values of the true error of the same observed value, and the reproduction weight is the weight of the observed value calculated by using the reproduction variance of the observed value; the reproduction variance, the average value of the reproduction variance, and the reproduction right of the different observations are calculated according to the formulas (19), (20), and (21), respectively:
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